On model structure testing in system identification

In system identification it is assumed in many cases that the order of the system is known. Thus it is important to perform tests for determining the correct model order. For a single-input, single-output system the order is the only structural parameter, but for multivariable systems there are several structural parameters. It is in such cases not enough to test only for the order but to investigate if a model structure is appropriate or not. The paper contains a brief review of some methods for model structure testing. Two methods proposed by Akaike and the F-test are compared and it is shown that they are asymptotically equivalent. The methods are analysed theoretically through analytical calculations. The results are also illustrated with simulations.